What are the differences between Sierpinski/Vicsek fractals?

In summary, Sierpinski and Vicsek fractals are both self-similar geometric patterns, but they differ in their construction methods and overall shapes. Sierpinski fractals are created by dividing an equilateral triangle, while Vicsek fractals are made by dividing a square. Sierpinski fractals have a three-dimensional pyramid shape, while Vicsek fractals have a two-dimensional cross shape. Additionally, Sierpinski fractals have a non-integer fractal dimension, while Vicsek fractals have an integer fractal dimension. Both types can be found in nature, but Sierpinski fractals are more commonly seen in natural structures like crystals and fern leaves.
  • #1
qnach
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What are the differences between Sierpinski/Vicsek fractals?
 
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  • #3
jedishrfu said:
Have you tried a google search?

I found this wiki article explaining how they are generated.

https://en.m.wikipedia.org/wiki/N-flake

There are also some fractal videos that you can checkout too that may explain it better.

Very unfortunately the website you mentioned did not compare them.
It mentioned only their name.
 
  • #4
Yes so I guess you can use google yourself to find out more.
 
  • #5
qnach said:
Very unfortunately the website you mentioned did not compare them.
You must not have read very far. The site that @jedishrfu mentioned describes each of them in detail, with images and how they are produced.

qnach said:
It mentioned only their name.
Not true. Take a closer look this time.
 
  • #6
Thread closed due to substandard original post.
 

What are the differences between Sierpinski and Vicsek fractals?

Sierpinski and Vicsek fractals are both types of self-similar geometric patterns, but they are different in a few ways:

How are Sierpinski and Vicsek fractals constructed?

Sierpinski fractals are created by repeatedly dividing an equilateral triangle into four smaller triangles, while Vicsek fractals are made by dividing a square into nine smaller squares and removing the center square.

What is the overall shape of a Sierpinski fractal compared to a Vicsek fractal?

A Sierpinski fractal has a three-dimensional pyramid shape, while a Vicsek fractal has a two-dimensional cross shape.

Do Sierpinski and Vicsek fractals have different mathematical properties?

Yes, Sierpinski fractals have a non-integer fractal dimension of approximately 1.585, while Vicsek fractals have an integer fractal dimension of 2.

Which type of fractal is more commonly found in nature?

Both Sierpinski and Vicsek fractals can be found in natural phenomena, but Sierpinski fractals are more commonly seen in natural structures like crystals and fern leaves.

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